1210.4774 (Hosho Katsura et al.)

Nagaoka states in the SU($n$) Hubbard model    [PDF]

Hosho Katsura, Akinori Tanaka

We present an extension of Nagaoka's theorem in the SU($n$) generalization of the infinite-$U$ Hubbard model. It is shown that, when there is exactly one hole, the fully polarized states analogous to the ferromagnetic states in the SU(2) Hubbard model are ground states. For a restricted class of models satisfying the connectivity condition, these fully polarized states are the unique ground states up to the trivial degeneracy due to the SU($n$) symmetry. We also give examples of lattices in which the connectivity condition can be verified explicitly. The examples include the triangular, kagome, and the hypercubic lattices in $d (\ge 2)$ dimensions, among which $d=2$ and 3 cases are experimentally realizable in ultracold atomic gases loaded into optical lattices.

View original: http://arxiv.org/abs/1210.4774